Lattice field theories with an energy current

TL;DR

This paper studies a lattice scalar field model under bias favoring energy current, revealing a phase transition to a current-carrying phase with quantum effects allowing current at minimal bias.

Contribution

It introduces a non-equilibrium lattice scalar field model with quantum effects, showing novel phase transition behaviors in energy current establishment.

Findings

Transition to a gapless modulated phase at finite bias

Quantum effects enable non-zero current at small bias

Different transition orders in ferromagnetic and disordered phases

Abstract

We investigate a lattice scalar field theory in the presence of a bias favouring the establishment of an energy current, as a model for stationary nonequilibrium processes at low temperature in a non-integrable system. There is a transition at a finite value of the bias to a gapless modulated phase which carries a classical current; however, unlike in similar, integrable, models, quantum effects also allow for a non-zero current at arbitrarily small bias. The transition is second order in the magnetically disordered phase, but is pre-empted by a first-order transition in the ferromagnetic case, at least at the mean-field level.